The TIGER model simulates a swimming bacterium using a dynamically coupled fluid–structure approach. The head is modeled as a rigid ellipsoid while the flagellar tail oscillates as a curved arc whose momentum is projected into a surrounding 3D fluid lattice. Fluid dynamics are solved using the Lattice Boltzmann Method (LBM) on a D3Q19 grid, allowing for fine-grained modeling of velocity flow fields around the microbe. At each timestep, momentum from the moving tail segments is injected into the fluid, producing biologically realistic propulsion. This platform builds on previous work which quantified how motility enhances encounter rates in complex media ( Joiner et al., 2019 ). TIGER extends that framework to resolve full 3D velocity fields, centerline trajectories, and animated hydrodynamic visualizations suitable for both research and education.
Figure 1. Fluid motion around a swimming bacterium simulated by the TIGER model. Momentum from the flagellar tail is injected into a 3D grid, generating propulsion patterns visualized in the velocity field.
To model mesoscale fluid dynamics around the bacterium, the TIGER simulation uses the Lattice Boltzmann Method (LBM) on a D3Q19 lattice. Instead of solving the Navier-Stokes equations directly, the LBM evolves fluid component \(i\) at location \( \vec{x} \), with microscale velocity \( \vec{c} \), from time \( t \) to \( t_f \) using a simplified distribution function \( f_i (\vec{x}, \vec{c}, t) \). The evolution of \( f_i \) follows the discrete Boltzmann equation towards its equilibrium distribution \(f_i^{eq}\).
\[ \begin{aligned} f_i \,(\vec{x} + \vec{c}\, \Delta t \,, t + \Delta t) = f_i - \frac{\Delta t}{\tau_f}\left( f_i^{eq} - f_i \right), \end{aligned} \]The macroscopic velocity \( \vec{u} \) and density \( \rho \) are recovered by summing over directions: \[ \rho = \sum_i f_i, \quad \vec{u} = \frac{1}{\rho} \sum_i f_i \, \vec{c}_i \] The TIGER model leverages this framework to resolve complex interactions between the bacterium and its surrounding flow field. By integrating structure-driven propulsion with LBM-based fluid dynamics, the simulation achieves biologically realistic fluid motion in a computationally tractable form. The TIGER framework is extensible to a wide range of swimmer geometries and boundary conditions, including confined and obstacle-laden environments. This flexibility enables simulation of microbial navigation, biofilm interactions, and emergent hydrodynamic coupling at micron scales.
Figure 2. Cross-sectional visualization of the simulated 3D fluid velocity field generated using the TIGER model.
To interpret fluid dynamics at each timestep, we extract 2D velocity field slices from the full 3D simulation domain. The panels shown right show four diagnostic views: left and right slices through the bacteriumy y -axis, and front and back slices through the y-axis. These heatmaps reveal the spatial distribution of velocity magnitude, with brighter regions indicating areas of stronger flow. The bacterium's head and flagellum create distinct flow structures, including zones of high vorticity and recirculation. This cross-sectional visualization highlights how localized tail propulsion drives momentum into the surrounding fluid, enabling a rich dynamic that varies over time and orientation. These heatmaps serve as diagnostic tools, revealing gradients in local fluid velocity and capturing the effects of bacterium-driven fluid excitation. Notably, the simulation resolves zones of recirculating flow and anisotropic momentum transfer, which emerge due to the nonlinear coupling between swimmer geometry and tail kinematics. The observed patterns support a time-varying propulsion regime, wherein local velocity magnitude evolves as a function of tail phase angle and spatial orientation. Letting \( \|\vec{u}(x,y)\| \) represent the in-plane velocity magnitude, the TIGER model maps each slice as \( \|\vec{u}\| = \sqrt{u_x^{\,2} + u_y^{\,2}} \), enabling analysis of rotational symmetry and deformation over time. These visualizations highlight the strength of TIGER as a diagnostic platform, capable of producing high-resolution insight into microbial fluid dynamics.